Finite Group Databasebeta

← #20254387

Subgroups — #20254387

Order 6016.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094012C211yesmaximal, characteristic
2#15689515C212yesmaximal, complemented
3#15689485C212yesmaximal, complemented
4#15689345C214yesmaximal, complemented
5#15689278C212yesmaximal, complemented
6#15689273C212yesmaximal
7#15689180C211yesmaximal, characteristic, complemented
8C47×#533C211yesmaximal, characteristic, complemented
9C22×Dic94C2211yescharacteristic
10C22×D188C2211yescharacteristic
11C2×#10625337C2214yescomplemented
12C2×#10625336C2214yes—
13#13094012—21no—
14#13094012—21no—
15#13094012C2212yes—
16#13094012C2212yes—
17C2×(C2×D47)⋊C4—21no—
18C2×(C2×D47)⋊C4—21no—
19C4⋊(C47⋊C8)C2212yescomplemented
20#13093947C2214yescomplemented
21#13093944C2214yes—
22C22⋊(C47⋊C8)C2212yes—
23#13093935C2212yescomplemented
24C4⋊Q8×C47C2211yescharacteristic, complemented
25C4⋊Q8×C47C2211yescharacteristic, complemented
26#125×C47—21no—
27C22⋊Q8×C47—21no—
28C22⋊Q8×C47C2212yes—
29C4×Q8×C47—21no—
30C4×Q8×C47C2212yescomplemented
31#117×C47—21no—
32C2×C42×C47C2211yescharacteristic
33C23×D47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47C2312yes—
36C22×C4×C47D411yescharacteristic
37C22×C4×C47D411yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C2×D188—21no—
41C2×D188—42no—
42C2×D188C2312yes—
43C2×Dic94—21no—
44C2×Dic94—42no—
45C2×Dic94C2312yes—
46C4⋊C4×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47C2312yes—
52C22⋊C4×C47—22no—
53C42×C47—22no—
54C42×C47D411yescharacteristic
55C42×C47D411yescharacteristic
56C42×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58#10625337—44no—
59#10625336—44no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64C2×C47⋊C8C2314yes—
65C23×C47C2×D411yescharacteristic
66C22×D47—22no—
67C22×D47—42no—
68C22×D47—42no—
69C22×D47—42no—
70Q8×C47—24no—
71Q8×C47—42no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—41no—
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—22no—
84C2×Dic47—42no—
85D188—24no—
86D188—42no—
87Dic94—24no—
88Dic94—42no—
89C47⋊C8—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#13712yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—84no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47H(5,𝔽2)12yes—
106Dic47—42no—
107#3215—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47#53511yescharacteristic
110C2×C47C2×#13711yescharacteristic
111C2×C47#57511yescharacteristic
112D47—82no—
113#533D4711yescharacteristic, complemented
114C2×#124—471no—
115#497—472no—
116#489—472no—
117#464—474no—
118#451—472no—
119#450—472no—
120#432—471no—
121C47#321511yescharacteristic, complemented, Sylow
122C22×Q8—471no—
123C22×D4—471no—
124C2×Q16—474no—
125C2×SD16—474no—
126C4⋊Q8C2×D4711yescharacteristic, complemented
127C4⋊Q8C2×D4711yescharacteristic, complemented
128#125—21no—
129#124—472no—
130#124—472no—
131#124—941no—
132#124—941no—
133C22⋊Q8—21no—
134C22⋊Q8C2×D4712yes—
135C4×Q8—21no—
136C4×Q8C2×D4712yescomplemented
137#117—21no—
138C2×C22⋊C4—941no—
139C2×C22⋊C4—941no—
140C2×C42C2×D4711yescharacteristic
141C4⋊C8—472no—
142#103—474no—
143#102—474no—
144C22⋊C8—472no—
145#97—472no—
146C24—941no—
147C2×Q8—21no—
148C2×Q8—472no—
149C2×Q8—941no—
150C2×Q8—1882no—
151C2×Q8C22×D4712yes—
152C2×D4—472no—
153C2×D4—941no—
154C2×D4—1882no—
155C22×C4—941no—
156C22×C4C22⋊D4711yescharacteristic
157C22×C4C22⋊D4711yescharacteristic
158C22×C4C22×D4711yescharacteristic
159Q16—1884no—
160SD16—1884no—
161C2×C8—474no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4C22×D4712yes—
168C22⋊C4—22no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C42—22no—
174C42C22⋊D4711yescharacteristic
175C42C22⋊D4711yescharacteristic
176C42C22×D4711yescharacteristic
177C42C22×D4711yescharacteristic
178C23—942no—
179C23—1882no—
180C23—1882no—
181C23—1882no—
182C23C2×C22⋊D4711yescharacteristic
183Q8—24no—
184Q8—42no—
185Q8—944no—
186Q8—1882no—
187D4—944no—
188D4—1882no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—942no—
195C2×C4—1882no—
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C2×C4C2×C22⋊D4711yescharacteristic
200C2×C4C2×C22⋊D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—944no—
203C22—21no—
204C22—21no—
205C22—3764no—
206C22—1882no—
207C22—1882no—
208C22—1882no—
209C22#1309405512yes—
210C22C22×C22⋊D4711yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—1882no—
219C4#1309407012yes—
220C2—22no—
221C2—3762no—
222C2#1568968711yescharacteristic
223C2C2×#1309405511yescharacteristic
224C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#533C2
socleC22×C47C22×D4
hypercenter#533D47
hypocenterC47#3215
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #15689515C2semidirect
3. #15689485C2semidirect
4. #15689345C2semidirect
5. #15689278C2semidirect
7. #15689180C2semidirect
8. C47×#533C2semidirect
11. C2×#10625337C22semidirect
19. C4⋊(C47⋊C8)C22semidirect
20. #13093947C22semidirect
23. #13093935C22semidirect
24. C4⋊Q8×C47C22semidirect
25. C4⋊Q8×C47C22semidirect
30. C4×Q8×C47C22semidirect
113. #533D47semidirect
121. C47#3215semidirect
126. C4⋊Q8C2×D47semidirect
127. C4⋊Q8C2×D47semidirect
136. C4×Q8C2×D47semidirect